Rethinking reliability in neural operators through residual and agent-based corrections

A neural operator trained to emulate a boundary-value problem is usually judged by its error on held-out data. That number says little about the quantity a user actually cares about: whether the surrogate can be substituted for the solver inside an optimization or an inference loop without changing the answer. In the topology-optimization setting the gap is stark: surrogates with respectable test error produced minimizers as much as 80% away from the true design.

This talk takes the position that reliability should be built in after training rather than pursued only through larger models and more data. Using the residual of the governing equations and its tangent, a correction step repairs the surrogate’s prediction at the point where it is being used, and brings the same minimizer error below 7%. The residual is available without new labels, which is what makes the correction practical. The talk closes on agent-based variants, which decide when a correction, or a full solve, is worth its cost.